Question 300288
The solution to this system solves the intersection of a circle and a line. 
{{{drawing(300,300,-6,6,-6,6,grid(1),circle(0,0,5), graph( 300, 300, -6, 6, -6, 6, -2x+10)) }}} 
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1.{{{x^2+y^2=25}}}
2.{{{2x+y=10}}}
From eq. 2,
{{{y=-2x+10}}}
{{{y^2=(-2x+10)^2}}}
{{{y^2=4x^2-40x+100}}}
Substitute into eq. 1,
{{{x^2+y^2=25}}}
{{{x^2+4x^2-40x+100=25}}}
{{{5x^2-40x+100=25}}}
{{{5x^2-40x+75=0}}}
{{{x^2-8x+15=0}}}
Factor,
{{{(x-3)(x-5)=0}}}
Two solutions:
{{{x-3=0}}}

{{{x=3}}}

Then using eq. 2,
{{{ 2x+y=10}}}
{{{6+y=10}}}
{{{y=4}}}
(3,4)
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{{{x-5=0}}}

{{{x=5}}}

{{{10+y=10 }}}
{{{y=0}}}
(5,0)
The solution is verified by the previous graph.